Question 1099788
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Find the line which goes through the point (2,-5) and is perpendicular to the line 3y-7x=2.  
(write the numerical coefficient of each term to complete the required equation
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<pre>
The given line 3y - 7x = 2  is  y = {{{(7x + 2)/3}}}  and has the slope {{{7/3}}}.


Hence, the perpendicular line has the slope  {{{-3/7}}}, which is reciprocal with the opposite sign.


The the equation of this perpendicular line passing through the point (2,-5) is 

y - (-5) = {{{(-3/7)*(x-2)}}}.


Multiply both sides by 7.  You will get

7y + 35 = -3(x-2),   or   7y + 35 = -3x + 6,   or finally

3x + 7y = -29.
</pre>


{{{graph( 330, 330, -5.5, 5.5, -5.5, 5.5,
          (7x + 2)/3, (-3/7)*(x-2) - 5
)}}}


The line 3y - 7x = 2 (original line, red)  and the line 3x + 7y = -29 (perpendicular passing through (2,-5), green)


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The solution by @josgarithmetic is <U>W R O N G</U>.  Simply ignore it.